MinT - Best Known (19−15, 19, s)-Nets in Base 256

Best Known (19−15, 19, s)-Nets in Base 256

(19−15, 19, 261)-Net over F₂₅₆ — Constructive and digital

Digital (4, 19, 261)-net over F₂₅₆, using

net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(19−15, 19, 321)-Net over F₂₅₆ — Digital

Digital (4, 19, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 19, 321)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
    - sharp bound on the number of rational points on curves with genus 2 [i]

(19−15, 19, 20650)-Net in Base 256 — Upper bound on s

There is no (4, 19, 20651)-net in base 256, because

1 times m-reduction [i] would yield (4, 18, 20651)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 22 304061 866222 970312 107808 910309 796587 096936 > 256¹⁸ [i]